A quantile regression approach to define optimal ecological niche (habitat suitability) of cockle populations (Cerastoderma edule)

SUPPLEMENTARY DATA

1 Introduction

2 Materials and Methods

All data processing was conducted in R version 4.3.0 (2023-04-21 ucrt) except for MARS 3D pre-treatment in Matlab 2019a. Significance levels are p < .0001 with “****”, p < .001 with “***”, p < .01 with “**”, p < .05 with “*”.

2.1 Study area

Several historically known areas of the Seine estuary with different habitats or communities were studied, mainly mudflats and subtidal areas (Figure 1).

Figure 1: Maps of habitats areas defined in the study area. Dots represent the location of the biological samples

2.2 Biological model

2.3 Datasets

2.3.1 Biological data

2.3.2 Hydro-Morpho-Sedimentary data

2.3.3 Calculation and selection of predictors

Figure 2: Correlation plot of all variables extracted from MARS3D dataset corresponding to biomass and densities from biological dataset. Correlation scores are shown above the diagonal, scatter plots with a linear regression below the diagonal, while the diagonal itself shows the density plot of each variable.

3 Results

3.1 Description of the biological data set

Figure 3: C. edule population biomass [gAFDW/m²] and density [ind/m²] in the Seine estuary, by period for each area (A) and by areas for each period (B). Dots represent the mean and standard error of each sub-group.

3.2 Description of the hydro-morpho-sedimentary data set

Map

Figure 4: Mars3D selected factors maps in the Seine estuary

Density plots

Figure 5: Mars3D selected factors density plot in the Seine estuary

daily maximum current speed (m.s-1)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

inundation time (%)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

daily salinity range (u.s.i)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

temperature (degC)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

mud content (%)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

daily maximum bed shear stress (N.m-2)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

bathymetry (m)

Mars3D selected factors distribution in the Seine estuary, by Period for each area (A) and by areas for each Period (B)

3.3 Methodology assessment

Figure 6: ∆AICc comparison for all SDMs computed, according to the quantile, the type of model and the response.

Figure 7: Example of modelled vs observed data plotted for each model based on biomass under set A. The black line represents the 1:1 ratio.

Figure 8: Examples of SDM surface plots under set A: linear with interaction (A), Gaussian non-linear (B) and Cubic B-Spline linear (C). The upper panel shows the surfaces side by side, the lower panel shows the 3D plots with all processed quantiles superposed. The biological data observed with this model are represented by a contour plot, the data over the model are represented by red stars.

Figure 9: SDM interactive 3D plots

Figure 10: SDM interactive 3D plots

Figure 11: SDM interactive 3D plots

3.4 Species Distribution Models – Optimal Ecological Niche (SDM)

3.4.1 Comparison of linear and nonlinear Quantile Regression

Biomass

Sets computed with linear model (top row, numbered 1) and non-linear with a? the? Gaussian equation (bottom row, numbered 2), the observed biological data under the model surface are represented by an isometric curve, the data over the model are represented by red stars. Each pair has its own scale to ensure visibility

Density

Sets computed with linear model (top row, numbered 1) and non-linear with a? the? Gaussian equation (bottom row, numbered 2), the observed biological data under the model surface are represented by an isometric curve, the data over the model are represented by red stars. Each pair has its own scale to ensure visibility

Biomass

Modelled vs observed data plot for RQ2int and RQ2nli SDM. Black line represents the 1:1 ratio

Density

Modelled vs observed data plot for RQ2int and RQ2nli SDM. Black line represents the 1:1 ratio

Biomass

Sets computed with linear with interaction (top, numbered 1) and nonlinear with gaussian equation (bottom numbered 2), the contour plot represents the observed HMS data

Density

Sets computed with linear with interaction (top, numbered 1) and nonlinear with gaussian equation (bottom numbered 2), the contour plot represents the observed HMS data

3.4.1.1 Interactive 3D SDM visualisation

Only RQ2nli SDM were represented, with all quantiles representation :

Only the chosen quantile :

3.4.2 Non-linear quantile regression with bifactorial Gaussian equation models

3.4.2.1 Application maps

Biomass

SDM models applied on the Seine estuary over the five periods.

Density

SDM models applied on the Seine estuary over the five periods.

3.4.2.2 Suitability index

Biomass

Suitability index per period and per area for all SDM models with a 95% confidence interval on means.

Density

Suitability index per period and per area for all SDM models with a 95% confidence interval on means.

3.4.2.3 Application density plots

Biomass

Density plot of the two predictors and the SDM model result in each area and in each period. The dots are the 95th quantile of the observed data.

Density

Density plot of the two predictors and the SDM model result in each area and in each period. The dots are the 95th quantile of the observed data.

3.4.2.4 Application density plot details

The four models result on the estuary regarding Areas and Periods, with the two calculation modes, for both responses.

3.4.2.4.1 Biomass

RQ2nli_11112

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11134

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11137

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11156

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

3.4.2.4.2 Density

RQ2nli_11212

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11234

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11237

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

RQ2nli_11256

Density plot of the two predictors and the SDM model result on each area and period. The dots were the 95th quantile of the observed data.

3.5 Results table

BiomassModel_\tau=A.e^{-[\frac{(x1-{\mu1}_\tau)^2}{2.{\sigma2}_\tau^2}+\frac{(x2-{\mu2}_\tau)^2}{2.{\sigma1}_\tau^2}]}

Table 1:

SDM model parameters for biomass response at tau=0.95

Abiotic factors	Estimate					Std. Error					Delta_AICc
	A	mu1	sigma1	mu2	sigma2	A	mu1	sigma1	mu2	sigma2
daily maximum current speed (m.s-1) * inundation time (%)	3090.872	-2.012	0.965	1.333	0.367	70,455.453	15.886	2.832	0.949	0.297	1,556.1
daily salinity range (u.s.i) * temperature (degC)	105.237	-3.850	7.619	12.322****	1.136·	388.07	44.777	17.489	1.05	0.628	1,641.9
daily salinity range (u.s.i) * bathymetry (m)	1085.680	-26.264	13.251	5.282	2.890	40,757.535	411.21	84.642	3.647	1.775	1,560
mud content (%) * daily maximum bed shear stress (N.m-2)	107.047·	0.355****	0.263*	1.261*	1.016**	56.763	0.064	0.104	0.571	0.31	1,470.2
·p<.1; *p<0.05; **p<0.01; ***p<0.001; ****p<0.0001

4 Supplementary data

4.1 Session information

Expand for R Session Info

─ Session info ───────────────────────────────────────────────────────────────
 setting  value
 version  R version 4.3.0 (2023-04-21 ucrt)
 os       Windows 10 x64 (build 19045)
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 ui       RTerm
 language EN
 collate  French_France.utf8
 ctype    French_France.utf8
 tz       Europe/Paris
 date     2023-10-12
 pandoc   3.1.1 @ C:/Program Files/RStudio/resources/app/bin/quarto/bin/tools/ (via rmarkdown)
 quarto   1.3.361 @ C:\\Users\\LEHUEN~1\\AppData\\Local\\Programs\\Quarto\\bin\\quarto.exe

─ Packages ───────────────────────────────────────────────────────────────────
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 [1] C:/Users/lehuen201/AppData/Local/Programs/R/R-4.3.0/library

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The Scientific colour map batlow (Crameri 2018) is used in this study to prevent visual distortion of the data and exclusion of readers with colour­vision deficiencies (Crameri, Shephard, and Heron 2020).

References

Crameri, Fabio, Grace E. Shephard, and Philip J. Heron. 2020. “The Misuse of Colour in Science Communication.” Nature Communications 11 (1): 5444. https://doi.org/10.1038/s41467-020-19160-7.